Multicore parallel programming has some very difficult problems such as deadlocks during synchronizations and race conditions brought by concurrency. Added to the difficulty is the lack of a simple, well-accepted computing model for multicore architectures--because of that it is hard to develop powerful programming environments and debugging tools. To tackle the challenges, we promote a generalized stream computing model, inspired by previous researches on stream computing, that unifies parallelization strategies for programming language design, compiler design and operating system design. Our model provides a high-level abstraction in designing language constructs to convey concepts of concurrent operations, in organizing a program's runtime layout for parallel execution, and in scheduling concurrent instruction blocks through runtime and/or operating systems. In this paper, we give a high-level description of the proposed model: we define the foundation of the model, show its simplicity through algebraic/computational operation analysis, illustrate a programming framework enabled by the model, and demonstrate its potential through powerful design options for programming languages, compilers and operating systems.